1. Field of the Invention
The present invention relates to a shape measuring apparatus which measures the shape of a measurement target surface, an exposure apparatus which includes the shape measuring apparatus, and a computer which processes an interference signal provided from an interferometer to determine the shape of the measurement target surface.
2. Description of the Related Art
There have been known various methods of measuring the three-dimensional shape of a measurement target surface using light interference. Of these methods, a method using a white light interference scheme utilizes the fact that white light has low coherence, and is effective for performing precise measurement of the three-dimensional shape of the measurement target surface.
Various types of white light interference scheme exist, including Mirau, Michelson, and Linnik. One apparatus of the Mirau type of white light interference scheme is a three-dimensional surface structure analyzing microscope given the product series name “New View” and is commercially available from Zygo Corporation. The measurement principle of the three-dimensional surface structure analyzing microscope (interferometer) will be explained with reference to FIGS. 6 and 7.
As shown in FIG. 6, an objective lens 610 accommodates a half mirror 611 and internal reference mirror 612 which form reference light. In this microscope, the reference light interferes with measurement light reflected by a measurement target surface 620. As shown in FIG. 7, an interference image is formed on the image sensing plane of an image sensor 650 which is optically conjugate to the measurement target surface 620. A white light source 640 uses, for example, a halogen lamp. A driving unit 660 vertically drives the objective lens 610. The driving unit 660 controls a position sensor such as a capacitance sensor to detect the position of the objective lens 610, and controls a driving element such as a piezoelectric element to drive the objective lens 610, on the basis of the detection result. While the driving unit 660 changes the position (and consequently, the light path length of the measurement light) of the objective lens 610, the image sensor 650 senses an interference image at each position. A computer captures the interference image sensed by the image sensor 650, and executes frequency domain analysis processing to obtain the height data of the measurement target surface with a vertical resolution of 0.1 nm. This frequency domain analysis processing uses an FFT (Fast Fourier Transformation) called FDA (Frequency Domain Analysis). The detection range of the horizontal resolution is determined by the imaging magnification from the measurement target surface 620 to the image sensor 650, and the pixel pitch of the image sensor 650. U.S. Pat. No. 5,398,113 discloses this technique.
FIG. 8 illustrates a white light interference signal from a given pixel of the image sensor 650. This white light interference signal is also called an interferogram. The abscissa indicates the measurement value obtained by the capacitance sensor after driving the objective lens by the driving element such as a piezoelectric element. The ordinate indicates the output from the given pixel of the image sensor 650. The peak position of the white light interference signal is measured, and a measurement value which corresponds to it and is obtained by the position sensor such as a capacitance sensor serves as the height measurement value of the measurement target surface at the given pixel. Measuring the heights of the measurement target surface at all the pixels of the image sensor 650 allows three-dimensional shape measurement.
The above-described FDA method calculates the peak position of the contrast using the phase gradient of a Fourier spectrum.
In the white light interference scheme, the key to measurement resolution and precision lay in the accuracy of obtaining a position at which the light path difference is zero. In addition to the FDA method, several fringe analyzing methods have been proposed for doing so, such as a phase crossing method and a method of calculating the envelope of a white light interference fringe using a phase shift method or Fourier transformation method to obtain the zero-crossing point of the light path difference from the maximum position of the fringe contrast.
The above-described white light interference scheme uses light quite different from “white light” in practice. More specifically, most of apparatuses use light sources having spectral distributions that are hardly “white light” spectral distributions. FIG. 9 shows an example of the spectral distribution of a light source commercially available as a white LED. This white LED uses a blue laser as the original light source, and therefore exhibits a partially convex spectral distribution having a high light intensity peak around a wavelength of 440 nm and a light intensity peak around a wavelength of 580 nm in the wavelength range from 500 nm to 700 nm. The white light interference scheme using such a light source increases the coherence length of the white light interference signal shown in FIG. 8. Since the coherence property of the white light interference signal deviates from the original one, it cannot attain high contrast. This can be an obstacle to the achievement of high precision.
In addition to the light source, there are various factors which inhibit ideal white light interference. For example, the spectral transmittance characteristic of an optical system, the spectrophotoelectric conversion efficiency characteristic of a photoelectric converter, and the like increase the coherence length of the white light interference signal because they are not flat in the frequency region used. This makes it difficult to obtain a high-contrast white light interference signal.
The light source, optical system, and photoelectric converter required to generate ideal white light interference result in an enormous cost.